@inproceedings{9e438e6734a848a5ae915100a5e8c5fb,

title = "Uniqueness of standing-waves for a non-linear schr{\"o}dinger equation with three pure-power combinations in dimension one",

abstract = "We show that symmetric and positive profiles of ground-state standing-wave of the non-linear Schr{\"o}dinger equation are non-degenerate and unique up to a translation of the argument and multiplication by complex numbers in the unit sphere. The non-linear term is a combination of two or three pure-powers. The class of non-linearities satisfying the mentioned properties can be extended beyond two or three power combinations. Specifically, it is sufficient that an Euler differential inequality is satisfied and that a certain auxiliary function is such that the first local maximum is also an absolute maximum.",

author = "Daniele Garrisi and Vladimir Georgiev",

note = "Funding Information: D. Garrisi was supported by INHA UNIVERSITY Research Grant and by the London Mathematical Society through the Research in Pairs Scheme 4, Grant ref. 41753 in the project “Uniqueness and non-degeneracy of normalized standing-waves”. Funding Information: V. Georgiev was supported in part by Project 2017 “Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari” of INDAM, GNAMPA - Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project “Dinamica di equazioni nonlineari dispersive”, “Fondazione di Sardegna”, 2016. Funding Information: D. Garrisi was supported by INHA UNIVERSITY Research Grant and by the London Mathematical Society through the Research in Pairs Scheme 4, Grant ref. 41753 in the project ?Unique-ness and non-degeneracy of normalized standing-waves?. V. Georgiev was supported in part by Project 2017 ?Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari? of INDAM, GNAMPA-Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.; AMS Special Session on Spectral Calculus and Quasilinear Partial Differential Equations and PDE Analysis on Fluid Flows, 2017 ; Conference date: 05-01-2017 Through 07-01-2017",

year = "2019",

doi = "10.1090/conm/725/14555",

language = "English",

isbn = "9781470441098",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "137--148",

editor = "Shijun Zheng and Jerry Bona and Geng Chen and {Van Phan}, Tuoc and Marius Beceanu and Avy Soffer",

booktitle = "Nonlinear Dispersive Waves and Fluids",

address = "United States",

}